The Lumen

The lumen is the standard unit for the luminous flux of a light source. It is an SI derived unit based on the candela. It can be defined as the luminous flux emitted into unit solid angle (1 sr) by an isotropic point source having a luminous intensity of 1 candela. The unit lumen is then equal to cd x sr. The abbreviation is lm and the symbol is Φv. In terms of radiant power (also called radiant flux) it can be expressed as:

The luminous flux is the part of the power which is perceived as light by the human eye, and the figure 683 lumens/watt is based upon the sensitivity of the eye at 555 nm, the peak efficiency of the photopic (daylight) vision curve. The luminous efficacy is 1 at that frequency.

A typical 100 watt incandescent bulb has a luminous flux of about 1700 lumens.

Units for other quantities in photometry contain the lumen, such as the lux (lumens/meter2)

Luminous Flux

Luminous Flux (Φv) is energy per unit time (dQ/dt) that is radiated from a source over visible wavelengths. More specifically, it is energy radiated over wavelengths sensitive to the human eye, from about 330 nm to 780 nm. Thus, luminous flux is a weighted average of the Radiant Flux in the visible spectrum. It is a weighted average because the human eye does not respond equally to all visible wavelengths.

The sensitivity of the eye peaks at 555 nm and falls off to approximately 10-4 at 380 and 750 nm. This constitutes the range of daylight sensitivity, or photopic vision. The eye's nighttime sensitivity, called scotopic vision, shifts toward the blue end of the visible, peaking at 507 nm and falling to 10-4 at 340 and 670 nm.
This weighting factor, or luminous efficacy (Vλ), allows for conversion of Radiant Flux to Luminous Flux at any wavelength. In the photopic region, the peak at 555 nm is assigned a conversion value of 683 lumens per Watt. The lumen is the unit of luminous flux, and is defined in terms of the candela, an SI base unit like the meter or second. 1 lumen is defined to be 1/4π candela, the SI base unit of Luminous Intensity.

Since the eye does not see all wavelengths equally well, the efficacy curve is a very important way to determine the Luminous Flux from a source. The Luminous Flux from a monochromatic source producing light at a single wavelength is easiest to determine.

Φv = Φ *Vλ * (683 lm/W)

For instance, a 5 mW laser pointer using at a wavelength of 680 nm produces

Determining the Luminous Flux from a source radiating over a spectrum is more difficult. It is necessary to determine the Spectral Power Distribution for the particular source. Once that is done, it is necessary to calculate the Luminous Flux at each wavelength, or at regular intervals for continuous spectra. Adding up the flux at each wavelength gives a total flux produced by a source in the visible spectrum.

Some sources are easier to do this with than others. A standard incandescent lamp produces a continuous spectrum in the visible, and various intervals must be used to determine the Luminous Flux. For sources like a mercury vapor lamp, however, it is slightly easier. Mercury emits light primarily in a line spectrum. It emits radiant flux at 6 primary wavelengths. This makes it easier to determine the Luminous Flux of this lamp versus the incandescent.

Generally, it is not necessary to determine the luminous flux for yourself. It is commonly given for a lamp based on laboratory testing during manufacture. For instance, the Luminous Flux for a 100W incandescent lamp is approximately 1700 lm. We can use this information to extrapolate to similar lamps. Thus the average luminous efficacy for an incandescent lamp is about 17 lm/W. We can now use this as an approximation for similar incandescent sources at various wattages. Often times, the manufacturer will list 'initial lumens' in its data for a lamp. This is the Luminous Flux for that lamp. It is listed in this manner because as a lamp ages, its power distribution shifts slightly and no longer radiates at precisely the wavelengths it did at the time it was new. However, for all intents and purposes, 'initial lumens' may be used for Luminous Flux for any necessary calculation.